Microfluidic biochips are devices that are designed for high throughput screening
and hybridization in genomics, protein profiling in proteomics, and cell analysis in cytometry.
They are used in clinical diagnostics, pharmaceutics and forensics. The biochips
consist of a lithographically produced network of channels and reservoirs on top of a glass
or plastic plate. The idea is to transport the injected DNA or protein probes in the amount
of nanoliters along the network to a reservoir where the chemical analysis is performed.
Conventional biochips use external pumps to generate the fluid flow within the network. A
more precise control of the fluid flow can be achieved by piezoelectrically agitated surface
acoustic waves (SAW) generated by interdigital transducers on top of the chip, traveling
across the surface and entering the fluid filled channels. The fluid and SAW interaction
can be described by a mathematical model which consists of a coupling of the piezoelectric
equations and the compressible Navier-Stokes equations featuring processes that occur on
vastly different time scales. In this chapter, we follow a homogenization approach in order
to cope with the multiscale behavior of the coupled system that enables a separate treatment
of the fast and slowly varying processes. The resulting model equations are the basis for
the numerical simulation which is taken care of by implicit time stepping and finite element
discretizations in space. Finally, the need for a better efficiency and cost effectiveness of the
SAWdriven biochips in the sense of a significant speed-up and more favorable reliability of
the hybridization process requires an improved design which will also be addressed in this
chapter. In particular, the challenge to deal with the resulting large scale optimal control and
optimization problems can be met by the application of projection based model reduction
techniques.
Keywords: Clinical diagnostics, compressible Navier-Stokes equations, hybridization process, implicit
time stepping, interdigital transducers (IDT), labs-on-achip, Micro-Electro-Mechanical Systems (MEMS),
microfluidic biochips, optimal control problem, optimization problem, piezoelectric equations, protein profiling,
sub-millimeter scale, surface acoustic waves (SAW).
